Express your answer as a mixed number simplified to lowest terms. $17\dfrac{1}{4}-7\dfrac{2}{6} = {?}$
Simplify each fraction. $= {17\dfrac{1}{4}} - {7\dfrac{1}{3}}$ Find a common denominator for the fractions: $= {17\dfrac{3}{12}}-{7\dfrac{4}{12}}$ Convert ${17\dfrac{3}{12}}$ to ${16 + \dfrac{12}{12} + \dfrac{3}{12}}$ So the problem becomes: ${16\dfrac{15}{12}}-{7\dfrac{4}{12}}$ Separate the whole numbers from the fractional parts: $= {16} + {\dfrac{15}{12}} - {7} - {\dfrac{4}{12}}$ Bring the whole numbers together and the fractions together: $= {16} - {7} + {\dfrac{15}{12}} - {\dfrac{4}{12}}$ Subtract the whole numbers: $=9 + {\dfrac{15}{12}} - {\dfrac{4}{12}}$ Subtract the fractions: $= 9+\dfrac{11}{12}$ Combine the whole and fractional parts into a mixed number: $= 9\dfrac{11}{12}$